Prove that ` (1-sin^(2)theta)sec^(2)theta=1`

Prove the following trigonometric identities: (1-sin^(2)theta)sec^(2)theta=1( ii) cos^(2)theta(1+tan^(2)theta)=1

Prove that (sin^(2)theta+cos^(2)theta)/(sec^(2)theta-tan^(2)theta)=1

Prove that: (1+sec 2theta)(1+sec2^(2)theta)(1+sec2^(3)theta)...... xx )(1+sec2^(n)theta) = tan2^(n)theta* cot theta

Prove that : sec^(2)theta - cos^(2) theta = sin^(2)theta(sec^(2)theta + 1)

Prove that : sec^(2)theta - cos^(2) theta = sin^(2)theta(sec^(2)theta + 1)

Prove that , (1+sec 2 theta) (1+sec2^(2) theta)(1+ sec2^(3)theta)... ( 1+sec 2^(2) theta) = (tan 2^(n) theta)/tan theta

Prove that sec theta(1-sin theta)(sec theta+tan theta)=1

Prove that (i) (1- sin theta)/(1+ sin theta)=(sec theta - tan theta )^(2) (ii) ((1+cos theta))/((1- cos theta))= ("cosec" theta + cot theta)^(2)

Prove that : sqrt((1-sin theta)/(1+sin theta))= {(sec theta- tan theta, if -pi/2 < theta< pi/2), (-sec theta+ tan theta, if pi/2 < theta< (3 pi)/2):} .

Prove that following identities sec^(4)theta(1-sin^(4)theta)-2tan^(2)theta=1